I graduated from Yale College so I thought I'd check out their attitude and recruitment of homeschoolers. I also know that one of the big traditional homeschool sites was created by a fellow Yalie who was actually in my class at Yale (1980) although we didn't know each other.

Jon Shemitz has long maintained a site with a huge section on homeschooling (although his kids are grown) at Welcome - Jon's Homeschool Resources.

I read the following quote attributed to a Yale Admissions officer:

We see only a few homeschooled applicants, and we do occasionally admit a homeschooled student. Evaluation is usually difficult, however. It helps if the applicant has taken some college level courses, and we can get evaluations from those teachers. We are not keen on homeschooled students where the only evaluations come from parents and the only other information available consists of test scores.

I googled it and found it attributed to Dean dates from 2008 from a New York Times article:

I then emailed the Yale Admissions office and received the following from
Mark Dunn
Sr. Assistant Director of Admissions:

Thank you for your email. The Admissions Office does not track or publicize figures for homeschooled students, so unfortunately I will not be able to give you a breakdown of incoming students who were homeschooled. As you would imagine, there is great variety in the educational trajectories of incoming students, many of whom may have homeschooled for some if not all of their primary and secondary education.

To your second question, Dean Brenzel’s quote from the Choice Blog is certainly still accurate. The page on our website you referenced - http://admissions.yale.edu/home-schooled-applicants (which I quote below) - will be the best resource available for prospective applicants who are homeschooled.

Best regards,

Mark Dunn, Sr. Assistant Director of Admissions
Yale University Office of Undergraduate Admissions

Yale Policy Statement Toward Home-Schooled Students
Home-schooled applicants complete the same application as other students and must fulfill the same testing requirements. Because home-schooled students may lack standard measures of academic performance, they must try to provide comparable information in different ways. Here are a few suggestions for home-schoolers as they approach the application process:

Standardized test scores hold relatively more weight for home-schooled applicants. If you are a home-schooler and you feel confident about your ability to do well on the exams, we advise you to demonstrate your abilities in various areas by taking more than the required two SAT Subject Tests.
Letters of Recommendation

We require letters of recommendation for home-schooled applicants, including two from academic teachers and one from the ‘school counselor.’ Please do not present letters written only by your parents. We need additional objective evaluations from educators who have interacted with you - perhaps a teacher from a course you took at a local college, someone who has mentored you in a tutorial, the local librarian with whom you’ve discussed books over the years, someone in whose lab you have done research, etc. Letters from an online instructor are acceptable but can be difficult to evaluate, as the teacher often has not had direct contact with the student.
Strength of Program

We will look closely at the list of subjects pursued through your high school program, but as with any applicant, we do not specify the number of years you must spend on any particular subject. We look for strength in all the major disciplines across the high school curriculum. Many home-schooled students pursue some course work at a local college or high school and we are happy to consider grades and recommendations from those sources as well.
Personal Qualities

We look for evidence of social maturity from all our applicants and especially from home-schooled students. Your personal statement, interests and activities, and letters of recommendation should speak to your ability to integrate well with other students and tell us about your non-academic interests.